Small-angle and finite-amplitude pendulum
Models an ideal point mass on a rigid, massless suspension with constant g and no damping.
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Models an ideal point mass on a rigid, massless suspension with constant g and no damping. It compares the small-angle period with the full period computed by the AGM method for swings of 0 to 179°. 180° and full rotation are excluded, and the period depends on the amplitude.
Model, grammar and limits
Tsmall=2π√(L/g); Tfinite=Tsmall/AGM(1,cos(θ0/2))
Numbers can have up to 48 characters, with a decimal point or e, and no thousands separators. Curves use 2 to 501 samples plus up to 16 section endpoints. Use up to 32 forces or sources and up to 16 sections. Springs take 1 to 20 periods with at least 8 samples per period; pendulum angles run from 0 to 179°. Magnus covers −40 to 35 °C over water and −40 to 0 °C over ice; relative humidity 0 to 100%, pressure 5 to 200 kPa, and vapor pressure must be below total pressure. Backup is limited to 1 MiB. Invalid, non-unique or unresolved data are rejected.
Results are numerical idealizations in SI units, shown with up to 10 digits; CSV keeps the numeric values and units. 9.80665 m/s² is the conventional standard g, not local gravity. Uncertainty in your inputs or the model is not estimated, and nothing here is a physical approval.
Calculation and backup stay in this browser. Workers stop after 15 seconds, or when you edit, reset or cancel. Inputs are never uploaded or stored. Input data, formulas and filenames are never sent. Only with your optional consent, Refentra sends aggregate counts of actions and outcomes, without input content.
Use the chosen model
- Model, grammar and limits
Models an ideal point mass on a rigid, massless suspension with constant g and no damping. It compares the small-angle period with the full period computed by the AGM method for swings of 0 to 179°. 180° and full rotation are excluded, and the period depends on the amplitude.
- Calculate
Tsmall=2π√(L/g); Tfinite=Tsmall/AGM(1,cos(θ0/2)). Numbers can have up to 48 characters, with a decimal point or e, and no thousands separators. Curves use 2 to 501 samples plus up to 16 section endpoints. Use up to 32 forces or sources and up to 16 sections. Springs take 1 to 20 periods with at least 8 samples per period; pendulum angles run from 0 to 179°. Magnus covers −40 to 35 °C over water and −40 to 0 °C over ice; relative humidity 0 to 100%, pressure 5 to 200 kPa, and vapor pressure must be below total pressure. Backup is limited to 1 MiB. Invalid, non-unique or unresolved data are rejected.
- Download CSV report
Results are numerical idealizations in SI units, shown with up to 10 digits; CSV keeps the numeric values and units. 9.80665 m/s² is the conventional standard g, not local gravity. Uncertainty in your inputs or the model is not estimated, and nothing here is a physical approval. Calculation and backup stay in this browser. Workers stop after 15 seconds, or when you edit, reset or cancel. Inputs are never uploaded or stored. Input data, formulas and filenames are never sent. Only with your optional consent, Refentra sends aggregate counts of actions and outcomes, without input content.
Model questions
Model, grammar and limits
Models an ideal point mass on a rigid, massless suspension with constant g and no damping. It compares the small-angle period with the full period computed by the AGM method for swings of 0 to 179°. 180° and full rotation are excluded, and the period depends on the amplitude. Tsmall=2π√(L/g); Tfinite=Tsmall/AGM(1,cos(θ0/2))
Unit
Length; Own gravitational acceleration; Maximum pendulum angle; Curve sample count (1). Numbers can have up to 48 characters, with a decimal point or e, and no thousands separators. Curves use 2 to 501 samples plus up to 16 section endpoints. Use up to 32 forces or sources and up to 16 sections. Springs take 1 to 20 periods with at least 8 samples per period; pendulum angles run from 0 to 179°. Magnus covers −40 to 35 °C over water and −40 to 0 °C over ice; relative humidity 0 to 100%, pressure 5 to 200 kPa, and vapor pressure must be below total pressure. Backup is limited to 1 MiB. Invalid, non-unique or unresolved data are rejected.
Model results
Results are numerical idealizations in SI units, shown with up to 10 digits; CSV keeps the numeric values and units. 9.80665 m/s² is the conventional standard g, not local gravity. Uncertainty in your inputs or the model is not estimated, and nothing here is a physical approval.
Download input backup
Calculation and backup stay in this browser. Workers stop after 15 seconds, or when you edit, reset or cancel. Inputs are never uploaded or stored. Input data, formulas and filenames are never sent. Only with your optional consent, Refentra sends aggregate counts of actions and outcomes, without input content.